This is my interpretation of Jung's psychological functions:
Thinking: searches for true ideas.
Feeling: has feelings about people (or things).
Sensation: senses objects.
Intuition: perceives possibilities in the world.
Introversion = subjective, while extraversion = objective. What is subjective is what is inside the self, while what is objective is outside of ourselves.
If you look at my definitions of the functions, each contains an objective and a subjective component. Applying this to each function yields the following definitions:
Introverted thinking: searches for true ideas.
For the introverted thinker, the emphasis is on the ideas themselves as opposed to how true they are in the real world. However, as in all the functions, there is still emphasis on how they fit into the external world (their truth), but this is not the main emphasis. This is coherent with why Jung says that introverted thinkers try to fit the facts to fit the idea; the idea is of ultimate importance, while the facts are secondary. This makes the introverted thinker's thought process primarily theoretical.
Extraverted thinking: searches for true ideas.
Since extraverted thinking is primarily concerned with truth, facts are its main emphasis. Jung says that extraverted thinkers tend to rely heavily on facts in their thinking. It might also explain the socionics interpretation of extraverted thinking, for which extraverted thinkers are concerned with what works in practice, for what could be a greater testament to the external truth of an idea than how well it works in reality?
Introverted feeling: has strong feelings about people (or things).
Introverted feelers have strong ties to objects and people, but they notice their feelings towards these external things more than the things themselves, for the thing itself is objective, and introverted feelers are more aware of the subjective aspects of their attachments.
Extraverted feeling: has strong feelings about people (or things)
As extraverted feelers pay more attention to the objective factor, they tend to have strong ties to people. This is why they tend to be so social; people have great value in their world, so they do everything they can to engage them.
Introverted sensation: senses objects.
Introverted sensors are more aware of the sensations that objects produce than the objects themselves. I think that socionics captures my interpretation of introverted sensing the best. For example, types often seek comfort, and when you seek comfort, you are usually more interested in the sensation of comfort itself than the object that is causing it.
Extraverted sensation: senses objects.
Extraverted sensors are the most "objective" of all the types; not only are they interested in the real world, they are interested in the objects themselves that this world is comprised of. This leads extraverted sensors to be materialistic and aesthetic. Good food is not good only because it tastes good. It's good because it is considered a delicacy, as that gives the food its status as an object in the world.
Introverted intuition: perceives possibilities in the world.
Introverted intuition is essentially imagination. When you're imagining something, you usually aren't interested in the realization of the possibilities you're imagining as much as the possibilities themselves. For example, if you imagine yourself romantically embracing a woman, it's the possibility of this happening that makes it interesting, and yet it doesn't have to be realized in the real world. It happens entirely in your mind. Forecasting things is also like this, in the sense that when you forecast something, you are focusing on possibilities in the world, but you are not engaging the world in any way. All of it happens within the context of your mind and imagination.
Extraverted intuition: perceiving possibilities in the world.
For extraverted intuition it isn't the possibilities themselves that are interesting, but their realization in the real world; if it can't be made a reality it isn't interesting. For example, if an extraverted intuitive enthusiastically encounters the prospect of obtaining a new job, the job itself is what makes an impression on them. They might think of the money they'll make, the type of work they'll be doing, the new city they'll be living in, etc. Therefore, there is more of a tendency to try and make dreams a reality, as opposed to just dreaming without a purpose.
Now let's consider which system (either socionics or MBTT) best captures my interpretation of each function:
Ti: MBTT. INTPs, for example, are often interested in developing theories and seeing how the facts fit into the theory, whereas I_Tjs are more concerned with rules and strict logic, which is not far from my interpretation, but doesn't capture the essence of it.
Te: socionics. E_Tjs are very concerned with facts and procedures that work, whereas MBTT doesn't emphasize these aspects as much, and places emphasis on things that aren't as relevant, such as E_TJs having "strong" personalities.
Fi: MBTT. Both socionics and MBTT capture the essence of Fi, but often has a people and moral emphasis, which does not fit into my interpretation.
Fe: MBTT. As I said, Fe is the most people-oriented function, and MBTT makes note of the fact that E_FJs are very social, whereas this is not emphasized as much in socionics.
Si: socionics. I said that socionics captures this function well, and MBTT is far from the mark by associating Si with routine and monotonous activities.
Se: socionics. Neither system captures this function well, but socionics is closer, since can be materialistic and emphasize status.
Ni: socionics. Socionics focuses more on imagination, while MBTT Ni focuses on drive and vision.
Ne: socionics and MBTT equally. Both of these systems seem to note that Ne types are interested in the prospects of things.